Relative entropy8/24/2023 ![]() Yes, cracking a stolen hash is faster, but it's not what the average user should worry about. (Plausible attack on a weak remote web service. (You can add a few more bits to account for the fact that this is only one of a few common formats.) Uncommon (non-gibberish) base word ]Ĭaps? ]Ĭommon Substitutions ] On each row, the first panel explains the breakdown of a password, the second panel shows how long it would take for a computer to guess, and the third panel provides an example scene showing someone trying to remember the password.)) The comic is laid out with 6 panels arranged in a 3x2 grid. A set of boxes is used to indicate how many bits of entropy a section of the password provides. Sci.((The comic illustrates the relative strength of passwords assuming basic knowledge of the system used to generate them. Wigner, E.P., Yanase, M.M.: Information content of distributions. Wehrl, A.: General properties of entropy. Vershynina, A., Carlen, E., Lieb, E.: Strong subadditivity of quantum entropy. Umegaki, H.: Conditional expectation in an operator algebra. Simon, B.: Loewner’s Theorem on Monotone Matrix Functions (Springer, 2019) Ruskai, M.B.: Remarks on Kim’s strong subadditivity matrix inequality: extensions and equality conditions’’. Ruskai, M.B.: Another short and elementary proof of strong subadditivity of quantum entropy. ![]() Ruskai, M.B.: “Lieb’s simple proof of concavity of \( \) and remarks on related inequalities” Int. ![]() B.: “Inequalities for quantum entropy: a review with conditions for equality” J. Petz, D.: Monotone metrics on matrix spaces. Petz, D.: Quasi-entropies for finite quantum systems. Ohya, M., Petz, D.: Quantum Entropy and Its Use (Springer, 1993) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information (Cambridge University Press, 2000) Lieb, E.H., Ruskai, M.B.: Some operator inequalities of the Schwarz type. Lieb, E.H., Ruskai, M.B.: Proof of the strong subadditivity of quantum-mechanical entropy. Lieb, E., Ruskai, M.B.: A fundamental property of quantum-mechanical entropy. Lieb, E.H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Lesniewski, A., Ruskai, M.B.: Monotone Riemannian metrics and relative entropy on noncommutative probability spaces. Lanford, O., III., Robinson, D.W.: Mean entropy of states in quantum statistical mechanics. Kim, I.: Operator extension of strong subadditivity of entropy. Kiefer, J.: Optimum experimental designs. Jenčová, A., Ruskai, M.B.: A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality. Hiai, F., Ruskai, M.B.: Contraction coefficients for noisy quantum channels. Hasegawa, H.: \(\alpha \)-divergence of the noncommutative information geometry” Rep. 529, 73–140 (AMS, 2010)Įffros, E.G.: “A matrix convexity approach to some celebrated quantum inequalities’’. In the last two decades, information entropy measures have been relevantly applied in fuzzy clustering problems in order to regularize solutions by avoiding the formation of partitions with excessively overlapping clusters. I The relative entropy and mutual information concepts can be extended to the continuous case in a straightforward manner, and convey the same information Entropy and Mutual Information 2/24. : Trace inequalities and quantum entropy: an introductory course Contemp. : Topics on Operator Inequalities Sapporo Lecture Notes (1978)Īndo, T.: Concavity of certain maps on positive definite matrices and applications to Hadamard products.
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